From Wine to Water: Optimizing Description Logic Reasoning for Nominals

OWL-DL is a World Wide Web Consortium standard for representing ontologies on the Semantic Web. It can be seen as a syntactic variant of the Description Logic SHOIN (D), with an OWL-DL ontology corresponding to a SHOIN (D) knowledge base. The very recent accomplishment of a decision procedure for SHOIN (D) poses the challenge of turning the decision procedure into a practical implementation. In particular, we emphasize the need of new optimization techniques for nominals, especially in the presence of large number of individuals in the KB. In this paper, we present new techniques for optimizing DL reasoning in the presence of nominals in the TBox and individuals in a large ABox. We have integrated our optimizations in the open-source Pellet reasoner, which is sound and complete for SHOIN (D), and found that they suffice for efficiently classifying the famous Wine Ontology. We also show that these optimization techniques produce significant performance improvements in other widely used ontologies containing nominals, such as the OWL-S and AKT ontologies. Introduction and Motivation OWL-DL became a World Wide Web Consortium standard for representing ontologies on the Semantic Web in Feburary, 2004. As the W3C Web Ontology working group approached completion, there were two deep controversies with regard to the expressivity of the language: first, there was, at that point, no decision procedure for OWL-DL, a language many felt had decidabilty as its main justification, and, secondly, the example ontology in the OWL specifications (Smith, Welty, & McGuiness 2004), the Wine Ontology, which tried to exercise every feature of OWL-DL, was not processable by any existing or anticipated reasoner. Of particular concern were the presence of a large number of nominals, that is, individuals appearing in concept definitions. To the best of our knowledge, at the time, there were no reasoners that could handle nominals at all, even for the subsets OWL-DL where there were known decision procedures covering nominals. In this paper, we present a suite of ∗This author is is supported by the EU Project TONES (Thinking ONtologiES) ref: IST-007603. Copyright c © 2006, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. optimizations implemented in our OWL-DL reasoner, Pellet (Sirin et al. 2005), that suffice to render the Wine ontology (and most current ontologies with nominals) a solved problem. Our experiments show that without such optimizations reasoning with nominals is not practical at all. OWL-DL can be seen as a syntactic variant of the Description Logic SHOIN (D), with an OWL-DL ontology corresponding to a SHOIN (D) knowledge base 1. The logic SHOIN (D) is a decidable fragment of First Order Logic (FOL) and extends the Description Logic S (the DL providing transitive roles, all the boolean operators on concepts as well as existential and universal restrictions) with unqualified number restrictions (N ), nominals (O), inverses on roles (I), role hierarchies (H) and datatypes (D). Although tableau-based decision procedures for prominent fragments of SHOIN (D), such as SHIN (D) (Horrocks & Sattler 1999) and SHON (D) (Horrocks & Sattler 2001) have been known for quite a long time, the design of a decision procedure for SHOIN (D) has been accomplished only very recently (Horrocks & Sattler 2005). Expressive description logics, in particular the ones mentioned above, are known to have very high worst-case complexity. As a consequence, there exists a significant gap between the design of a decision procedure and the achievement of a practical implementation. Naive implementations are doomed to failure . In order to achieve acceptable performance, modern DL reasoners, such as FaCT, RACER, DLP and Pellet, implement a suite of optimization techniques (Horrocks 2003). These optimizations lead to a significant improvement in the empirical performance of the reasoner and have proved effective in wide variety of realistic applications. However, at the current stage of research and deployment, existing optimizations have been implemented and proved useful for the description logic SHIN (D). From an implementation point of view, the recent achievement of a decision procedure for SHOIN (D) poses new challenges: We refer the reader to (Horrocks & Sattler 2005) and (PatelSchneider, Hayes, & I.Horrocks 2004) for a detailed discussion of SHOIN and OWL-DL respectively. We also recommend (Horrocks, Patel-Schneider, & van Harmelen 2003) for a thorough discussion on the relationship between OWL and expressive Description Logics. • While many optimization techniques are completely independent of the DL supported by the reasoner, others are valid for certain logics only. In particular, some major optimizations for reasoning with large ABoxes rely on the absence of nominals in the definition of concepts. Moreover, in the presence of nominals, ABox assertions can affect concept satisfiability and TBox classification. In other words, nominals break the “separation” between TBox and ABox that traditionally existed in the implemented DLs. As a consequence, ontologies with nominals in the TBox and large number of instances in the ABox are likely to compromise the performance of DL reasoners. • Nominals are not supported by the state of the art DL reasoners, with the only exception of the Pellet system2. Thus, there is very little experience in developing techniques for dealing with nominals efficiently in practice. In particular, to the best of our knowledge, no optimizations specific for nominals have been designed and tested until now. From a logical point of view, the nominal constructor (Horrocks & Sattler 2001) (Schaerf 1994) transforms the object name o into the concept description {o}, which is evaluated, by every model-theoretic interpretation, to a singleton set with o as its only element. So far, nominals have been partially approximated in DL reasoners by treating them as pair-wise disjoint atomic concepts, commonly called pseudo-nominals. However, this technique is known to lead to incorrect inferences in some cases. From a modeling point of view, nominals are used in a significant number of ontologies available on the Semantic Web. The OWL-DL specification (Patel-Schneider, Hayes, & I.Horrocks 2004) contains two modeling constructs specific for nominals, which illustrate their main uses in Ontology Engineering. • The OneOf construct allows to define a concept by finite enumeration of its elements. For example, the atomic concept Continent can be defined, using nominals, as follows: Continent ≡ {europe, asia, america, antartica, africa, oceania} where the elements of the enumeration are individuals in the KB. • The hasValue construct is used as a shorthand for an existential restriction on a nominal concept. This construct can be used to describe catholics as persons who follow the Pope, or Rock’n’Roll fans as the persons who venerate Elvis: Catholic v Person u ∃follows.{pope} RockFan v Person u ∃hasIdol .{elvis} One prominent example of the use of nominals for modeling is the ontology used in the OWL documentation: the Wine Ontology (Smith, Welty, & McGuiness 2004). Very recently a new version of FaCT++ reasoner that supports nominals (but not ABoxes) was released. This ontology extensively relies on the OneOf and hasValue constructs for describing different kinds of wines according to various criteria, like the area they are produced in, the kinds of grapes they contain, their flavor and color, etc. For example, a “Cabernet Franc Wine” is defined to be a dry, red wine, with moderate flavor and medium body and which is made with Cabernet Franc grapes CabernetFranc ≡Wine u ≤ 1madeFrom u ∃madeFrom.{cabFrancGrape} CabernetFranc v ∃hasColor .{red} u ∃hasFlavor .{moderate} u